One type of connector includes a barrel for holding a body with passages that hold contacts (usually electrical contacts but possibly optical contacts). A coupling nut is rotatably mounted on the barrel so the nut can be rotated to thread it onto a mating second connector that has mating contacts. It is usually desirable to allow nut rotation with only a moderate resistance in a mating direction to mate the two connectors, and to provide a much higher resistance to nut rotation in the opposite unmating direction. One type of mechanism includes a ring that is mounted on the barrel and lies in the annular space between the barrel and nut, with the ring bent to form multiple closely-spaced ratchets that engage pins on the nut. The multiple closely spaced ratchets result in a ring with limited resilience and corresponding limited reliability. A resistance ring that could be easily placed in the annular space between the barrel and nut and that provided high resilience to reliably provide controlled resistance to nut rotation in each direction, would be of value.